2070 Asar · 14 marks

River discharge from two-point current meter data

Short answer

Mid-section method with v = 0.02×(60×rev/s)−0.02 and mean velocity from 0.2d and 0.8d points gives total discharge 211.3 m³/s. Q ≈ 211 m³/s.

Calculate the discharge of river section as given:

Distance (m)	1	2	3	4	6	8	12	16	17	18
Depth (m)	1	4.3	7.2	8.5	7.4	5.6	4.7	3.5	2.1	1.4
Revolution/s at 0.2d	1.4	1.0	2.6	2.9	2.7	2.5	2.3	2.1	1.8	1.5
Revolution/s at 0.8d	0.7	1.2	1.8	2.0	1.9	1.7	1.5	1.3	1.1	1.0

The current meter formula is $v = 0.02 N_s - 0.02$ , v = velocity (m/s) and $N_s$ = revolution per minute.

Method: mid-section method with the two-point velocity: $v_m=(v_{0.2}+v_{0.8})/2$ .

The meter equation is $v = 0.02N_s - 0.02$ with $N_s$ in revolutions per minute. The readings are in rev/s, so they are converted: $N_s = 60\times$ (rev/s). Example at 4 m, 0.2 d: $N_s = 2.9\times60 = 174$ rpm, $v = 0.02\times174-0.02 = 3.46$ m/s.

Strip width $w_i=(x_{i+1}-x_{i-1})/2$ ; the bank verticals at 0 m and 19 m have zero depth.

x (m)	d (m)	$v_{0.2}$	$v_{0.8}$	$v_m$	$w$ (m)	Area (m $^2$ )	$q$ (m $^3$ /s)
1	1	1.66	0.82	1.240	1	1.00	1.24
2	4.3	1.18	1.42	1.300	1	4.30	5.59
3	7.2	3.10	2.14	2.620	1	7.20	18.86
4	8.5	3.46	2.38	2.920	1.5	12.75	37.23
6	7.4	3.22	2.26	2.740	2	14.80	40.55
8	5.6	2.98	2.02	2.500	3	16.80	42.00
12	4.7	2.74	1.78	2.260	4	18.80	42.49
16	3.5	2.50	1.54	2.020	2.5	8.75	17.68
17	2.1	2.14	1.30	1.720	1	2.10	3.61
18	1.4	1.78	1.18	1.480	1	1.40	2.07
Total						87.90	211.3

Mean velocity $= 2.40$ m/s.

Answer: Discharge $Q \approx 211\ \text{m}^3/\text{s}$ .

✓ Answer checked by Claude Sonnet 5.5

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